A Monte-Carlo study of meanders

TL;DR

This paper uses Monte-Carlo simulations to analyze the statistical properties of meanders, providing asymptotic estimates of key parameters related to their shape and connectivity for large configurations.

Contribution

It introduces a novel Monte-Carlo method enabling simulation of large meanders up to n=400, leading to new asymptotic estimates of their statistical properties.

Findings

Connectivity per bridge R = 3.5018(3)

Configuration exponent gamma = 2.056(10)

Winding exponent nu = 0.518(2)

Abstract

We study the statistics of meanders, i.e. configurations of a road crossing a river through "n" bridges, and possibly winding around the source, as a toy model for compact folding of polymers. We introduce a Monte-Carlo method which allows us to simulate large meanders up to n = 400. By performing large "n" extrapolations, we give asymptotic estimates of the connectivity per bridge R = 3.5018(3), the configuration exponent gamma = 2.056(10), the winding exponent nu = 0.518(2) and other quantities describing the shape of meanders. Keywords : folding, meanders, Monte-Carlo, tree